The present invention relates generally to methods and systems used to process data pertaining to financial assets, such as loans, securities, and so forth. More particularly, the present invention relates to a method and system for estimating economic risk associated with a group of loans by determining future loan capital reserve requirements or other variables related to a group of loans using a mathematical Gaussian copula function.
In assessing and managing risks associated with a group of loans or other financial assets, it is often desirable to compute one or more variables associated with the group of loans. For example, in the secondary mortgage market, a mortgage investor may wish to compute such variables as initial and future loan capital reserve requirements. A capital reserve requirement is the amount of risk-free assets needed to be set aside to cover potential income shortfalls associated with a group of loans for a particular time period within a given probability. For example, the capital reserve requirement may be the amount of economic capital required to sustain a “stress loss” of 99.5% of cumulative losses associated with the pool of loans over a given 10-year period.
Computing such variables may often involve, for example, running a number of computer simulations based on one or more mathematical economic models or other associated equations to generate a number of statistical data paths (i.e., economic scenarios) representative of a range of projected economic conditions for a given time period. The statistical data paths may then be used to estimate a statistical distribution of one or more variables associated with the group of loans. These distributions may in turn be used to calculate further variables associated with the group of loans. For example, a mortgage investor may wish to determine the amount of economic capital required to sustain a stress loss of 99.5% of cumulative losses associated with a group of loans over an initial 10-year period by first simulating a number (e.g., 1000) of statistical data paths representing a range of projected economic conditions over a 10-year period, such as house price and interest rate paths based on predetermined mathematical house price or interest rate models. The mortgage investor may then further calculate one or more variables associated with the group of loans, such as, for example, periodic and cumulative default rate, prepayment rate, and severity of default, for each of the 1000 statistical data paths based on corresponding predetermined mathematical equations, and use these calculations to obtain statistical distributions pertaining to, for example, periodic and cumulative losses and unpaid loan balances. Given these distributions, the data path representing the worst 99.5% loss scenario (i.e., the “stress path”) may be determined, and economic capital reserve requirements may then be computed for the initial 10-year period.
The mortgage investor may then wish to further determine future loan capital reserve requirements for a subsequent time period, such as a 10-year period spanning years 2-11. However, due to changing economic conditions (e.g., increasing or decreasing house prices and interest rates) over time, using the original stress path may overstate or understate future loan capital reserve requirements for years 2-11, leading to inaccurate or inefficient assessment and management of the group of loans. To account for these changes, a new set of 1000 statistical data paths representative of projected economic conditions for years 2-11 could be generated for each of the original statistical data paths from which new parameter values could be calculated, and a new stress path could be determined from each of the 1000 new sets of 1000 simulations for each of the statistical data paths. A new loan capital reserve requirement could then be determined for years 2-11 that is dependent upon the first year economic conditions in each path while taking into account potential changes in economic conditions in the future. However, generating a new set of simulations for each of the original statistical data paths and calculating new variables for each new set of statistical data paths may be computationally infeasible for calculating changes in loan capital reserve requirements over time where significantly large loan portfolios or complex mathematical equations or models are involved, or where large numbers of simulations are necessary in order to maintain accuracy. Thus, there is a need for an improved method and system for estimating economic risk associated with a group of loans.